US 7023936 B2 Abstract Some embodiments of the present invention include a decoding system in which the decoding system uses iterative decoding techniques to decode signals encoded with lattice codes and/or multilevel coset codes. The decoding techniciucs according to some embodiments of the invention may be less complex than some decoding techniciues such as maximum likelihood decoding techniciues. Other embodiments of the prevent invention are described and claims.
Claims(32) 1. A method for decoding a signal, comprising:
determining prior probabilities associated with an encoded input signal;
performing iterative decoding on said encoded input signal, using said prior probabilities, to estimate a codeword associated with said encoded input signal, said codeword being within a base cell of an underlying lattice, wherein said encoded input signal is coded with a code having at least one constituent code, and wherein performing iterative decoding includes exchanging information between a plurality of constituent decoders during at least two iterative cycles when said encoded input signal includes multiple constituent codes; and
determining a cell translation associated with said encoded input signal based on said codeword.
2. The method of
3. The method of
said encoded input signal is coded with a multilevel coset code.
4. The method of
said encoded input signal is coded with a lattice code.
5. The method of
determining prior probabilities includes determining a probability that a first coordinate of a first constituent code has a predetermined value, based on said encoded input signal.
6. The method of
said encoded input signal has been modified by an interferer; and
determining prior probabilities includes determining probabilities based upon statistics associated with said interferer.
7. The method of
said statistics associated with said interferer are known.
8. The method of
determining prior probabilities includes assuming statistics for said interferer for use in determining said probabilities.
9. The method of
assuming statistics includes assuming that said interferer is uniformly distributed within a Voronoi cell of a lattice.
10. The method of
assuming statistics includes assuming that said Voronoi cell is a ball.
11. The method of
performing a first decoding iteration, using said prior probabilities, to generate first information; and
performing a second decoding iteration, using said first information, to generate second information.
12. A method for decoding a signal, comprising:
determining prior probabilities associated with an encoded input signal;
performing iterative decoding on said encoded input signal, using said prior probabilities, to estimate a codeword associated with said encoded input signal, said codeword being within a base cell of an underlying lattice, wherein performing iterative decoding includes exchanging information between a plurality of constituent; and
determining a cell translation associated with said encoded input signal based on said codeword.
13. The method of
exchanging information between a plurality of constituent decoders includes exchanging extrinsic infonnation.
14. A decoding system comprising:
a prior probability generator to generate prior probabilities associated with an encoded input signal;
an iterative decoding unit to determine a codeword associated with said encoded input signal by iterative decoding using said prior probabilities, said codeword being within a base cell of an underlying lattice, wherein said iterative decoding unit includes a plurality of constituent decoders, and wherein said constituent decoders are confi wired to exchanging information among said constituent decoders during said iterative decoding; and
a translation determination unit to determine a cell translation associated with said encoded input signal based on said codeword.
15. The decoding system of
a cell mapping unit to map said codeword to an appropriate cell of said underlying lattice using said cell translation.
16. The decoding system of
said encoded input signal is coded with a multilevel coset code.
17. The decoding system of
said encoded input signal is coded with a lattice code.
18. The decoding system of
said constituent decoders are configured to decode constituent codes of said encoded input signal.
19. A decoding system comprising:
a prior probability generator to generate prior probabilities associated with an encoded input signal;
an iterative decoding unit to determine a codeword associated with said encoded input signal by iterative decoding using said prior probabilities, said codeword being within a base cell of an underlying lattice, said iterative decoding unit including multiple constituent decoders to decode constituent codes of said encoded input signal wherein said constituent decoders are configured to exchange soft information between one another during said iterative decoding; and
a translation determination unit to determine a cell translation associated with said encoded input signal based on said codeword.
20. The decoding system of
at least one constituent decoder of said constituent decoders is an iterative decoder.
21. The decoding system of
at least one constituent decoder that is a soft in, soft out (SISO) decoder.
22. The decoding system of
said prior probability generator generates said prior probabilities based on known statistics associated with an interferer.
23. The decoding system of
said prior probability generator assumes statistics for an interferer and generates said prior probabilities based on said assumed statistics.
24. The decoding system of
said prior probability generator assumes that said interferer is uniformly distributed within a Voronoi cell of a lattice.
25. The decoding system of
said prior probability generator assumes that said Voronoi cell is a ball.
26. The decoding system of
said prior probability generator assumes that said interferer has a Gaussian distribution with zero mean and unknown variance.
27. An article comprising machine-accessible media having associated data, wherein the data, when accessed, results in a machine that performs a method for decoding a signal, said method comprising:
determining prior probabilities associated with an encoded input signal;
performing iterative decoding on said encoded input signal, using said prior probabilities, to estimate a codeword associated with said encoded input signal, said codeword being within a base cell of an underlying lattice, wherein said encoded input signal is coded with a code having at least one constituent code, and wherein performing iterative decoding includes exchanging information between a plurality of constituent decoders during at least two iterative cycles when said encoded input signal includes multiple constituent codes; and
determining a cell translation associated with said encoded input signal based on said codeword.
28. The article of
mapping said codeword to an appropriate cell of said underlying lattice using said cell translation.
29. The article of
said encoded input signal is coded with a multilevel coset code.
30. The article of
said encoded input signal is coded with a lattice code.
31. An article comprising machine-accessible media having associated data, wherein the data, when accessed, results in a machine that performs a method for decoding a signal, said method comprising:
determining prior probabilities associated with an encoded input signal;
performing iterative decoding on said encoded input signal, using said prior probabilities, to estimate a codeword associated with said encoded input signal, said codeword being within a base cell of an underlying lattice, wherein performing iterative decoding includes exchanging information between a plurality of constituent and decoders; and
determining a cell translation associated with said encoded input signal based on said codeword.
32. The article of
exchanging information includes exchanging extrinsic information between a plurality of constituent decoders.
Description The invention relates generally to signal decoding and, more particularly, to the decoding of signals that are encoded with lattice codes and/or multilevel coset codes. Maximum likelihood decoding represents an optimal solution for the decoding of signals encoded with multilevel coset codes and/or lattice codes. However, maximum likelihood decoding is not practical in many cases. For example, maximum likelihood decoding may not be practical when a code has a complex trellis. A complex trellis may exist, for example, when the number of constituent codes within a multilevel coset code or lattice code is large or when the minimal trellis of the constituent code(s) is large. Complex trellises are typically difficult to store (and draw) and, when maximum likelihood decoding is used, require a very large number of calculations to implement at the decoding stage. For this reason, decoding solutions are needed for multilevel coset codes and lattice codes that are less computationally complex than maximum likelihood decoding techniques. In the following detailed description, reference is made to the accompanying drawings that show, by way of illustration, specific embodiments in which the embodiments of the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the embodiments of the invention. It is to be understood that the various embodiments of the invention, although different, are not necessarily mutually exclusive. For example, a particular feature, structure, or characteristic described herein in connection with one embodiment may be implemented within other embodiments without departing from the spirit and scope of the invention. In addition, it is to be understood that the location or arrangement of individual elements within each disclosed embodiment may be modified without departing from the spirit and scope of the invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined only by the appended claims, appropriately interpreted, along with the full range of equivalents to which the claims are entitled. In the drawings, like numerals refer to the same or similar functionality throughout the several views. The present invention relates to methods and structures for decoding signals encoded with multilevel coset codes and/or lattice codes using iterative decoding techniques. The inventive techniques are significantly less computationally complex than optimal decoding solutions (e.g., maximum likelihood decoding) yet are capable of performance levels that approach those of the optimal methods. Because of the low complexity, the inventive techniques are especially valuable for use with codes having high dimensionality. In one embodiment, a data word received through a modulo lattice additive noise channel is treated as the sum of a multicode codeword and an interferer. The statistics of the interferer are used to determine prior probabilities associated with the multicode codeword. Iterative decoding techniques are then used to decode the individual constituent codes of the multicode codeword using the prior probabilities. The iterative decoding process may include, for example, the exchange of information (e.g., extrinsic information) between a number of constituent decoders. After the multicode codeword has been decoded, a cell translation is determined and used to map the multicode codeword to an appropriate underlying lattice cell. As used herein, the term “multicode” refers to the set of codewords of a multilevel coset code (or lattice code) that are within the base cell of an underlying lattice and the term “multicode codeword” will refer to a single codeword of the multicode. The inventive principles have application in communication systems and other systems using multilevel coset codes and/or lattice codes. A lattice must satisfy several rules; namely, it is closed under addition, it contains an inverse element for each lattice element, it contains the zero element (i.e., the origin of the coordinate axes is a point of the lattice), and it is discrete. Therefore, a lattice is a discrete infinite collection of points that is created by the repetition of a base or unit cell throughout space. A lattice code is a finite subset of a lattice. As such, a lattice code may be defined as the intersection of a lattice with a region of bounded support. A decoding rule that ignores the effect of a bounding region is referred to as lattice decoding. Other decoding rules exist that take the bounding region into account (e.g., minimum distance decoding). The inventive principles may be used in connection with both lattice decoding and minimum distance-like decoding techniques. Lattices can be constructed from one or more individual codes in a number of different ways (see, e.g., “Sphere Packings, Lattices and Groups” by J. H. Conway et al., pages 137–156 and 232–236, Springer-Verlag, New York, 1999). In one approach, for example, a point x=(x A coset code is a code of infinite codebook size that can be expressed as follows:
As illustrated in Using the input word {overscore (y)}, the prior probability generator In iterative decoding, there are typically two types of information concerning a bit of a codeword, information that depends on that bit's channel observation and information that depends on the channel observation of other bits that reflects to the subject bit due to the nature of the code. The latter type of information is referred to as “extrinsic information.” In one embodiment of the present invention, the prior probability generator
In one implementation, the above summations are truncated to include only the most significant terms. In the discussion above, the prior probabilities are expressed as conventional probabilities. It should be appreciated that the prior probabilities can be expressed in any of a number of alternative maimers in accordance with the embodiments of the invention including, for example, likelihood ratios, log likelihood ratios (LLRs), probability differences, and other similar formats. In at least one embodiment of the present invention, the iterative decoding unit The iterative decoding unit Referring back to The cell translation determination unit As an example of the operation of the decoding system In at least one embodiment of the present invention, turbo iterations are performed. That is, instead of determining {circumflex over ({overscore (r)} and {circumflex over ({overscore (λ)} once before generating the output word {overscore (x)}, a number of iterations are performed with each iteration further refining the previous one. In the above description, it was assumed that the statistics of the interferer {overscore (s)} were known. When no such statistical characterization of the interferer exists, however, other means for initializing the iterative process need to be developed. If a minimum Euclidean distance criterion is being used (i.e., the multilevel coset code point that is closest to {overscore (y)} in Euclidean distance is sought), then a number of initialization strategies are possible. In one approach, for example, it is assumed that the interferer has a Gaussian distribution with zero mean and unknown variance σ Once the prior probabilities have been determined, they are used to initialize an iterative decoding process for the input signal to estimate a multicode codeword {circumflex over ({overscore (r)} (block It should be appreciated that the principles of the embodiments of the present invention are not limited to use within communication systems. For example, any application that relies on vector quantization (e.g., speech or image compression) may benefit from the use of reduced complexity lattice decoders in accordance with the present invention. Other non-communications based applications are also possible. Although the embodiments of the present invention have been described in conjunction with certain embodiments, it is to be understood that modifications and variations may be resorted to without departing from the spirit and scope of the invention as those skilled in the art readily understand. Such modifications and variations are considered to be within the purview and scope of the invention and the appended claims. Patent Citations
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